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THE BOCHNER VANISHING THEOREMS ON THE CONFORMAL KILLING VECTOR FIELDS
Yıl 2019 ,
Cilt: 9 Sayı: 1, 114 - 120, 01.03.2019
S. Eker
Öz
In this paper, the result of the Bochner vanishing theorems, indicating the conditions that every conformal killing vector elds is parallel and there is no nontrivial Conformal Killing vector eld, are satised under two dierent modicated Ricci tensors.
Kaynakça
Bochner, S., (1946), Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52, 776-797.
Bochner, S. and Yano K., (1953), Curvature and Betti numbers, Ann. of Math. Stud., no. 32, Princeton Univ. Press.
Deshmukh, S., Al-Solamy FR., (2014), Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19, 86-93.
Jost, J., (2002), Riemannian Geometry and Geometric Analysis, Berlin, Germany: Springer-Verlag.
Kashiwada, T., (1968), On conformal Killing tensor, Natur. Sci. Rep. Ochanomizu Univ. 19, 67-74.
Kodaira, K., (1953), On a differential-geometric method in the theory of analytic stacks, Proc. Natl. Acad. Sci. USA 39, 1268-1273.
Lichnerowicz, A., (1958), Geometries des groupes de transformations, Paris, France: Dunod.
Lichnerowicz, A., (1948), Courboure et nombres de Betti dune variete riemannienne compacts, C.R. Acad. Sci. Paris 226, 1678-1680.
Lott, J., (2003), Some geometric properties of the Bakry- Emery- Ricci Tensor, Comment. Math. Helv. 78, 865-883.
Mogi, I., (1950), On harmonic field in Riemannian manifold, Kodai Math. Sem. Rep. 2, 61-66.
Tomonaga, Y., (1950), On Betti numbers of Riemannian spaces, J. Math. Soc. Japan 2, 93-104.
Murat, L., (2009), The Bochner technique and modification of the Ricci Tensor, Ann. Global Anal. Geom. 36, 285-291.
Petersen, P., (1998), Riemannian Geometry, New York, USA: Springer-Verlag.
Wei, G. and Wylie, W., (2009), Comparison geometry for the Bakry-Emery-Ricci tensor, J. Differential Geom. 83, 337-405.
Yano, K., (1952), On harmonic and Killing vector fields, Ann. of Math. 55, 38-45.
Yıl 2019 ,
Cilt: 9 Sayı: 1, 114 - 120, 01.03.2019
S. Eker
Kaynakça
Bochner, S., (1946), Vector fields and Ricci curvature. Bull. Amer. Math. Soc. 52, 776-797.
Bochner, S. and Yano K., (1953), Curvature and Betti numbers, Ann. of Math. Stud., no. 32, Princeton Univ. Press.
Deshmukh, S., Al-Solamy FR., (2014), Conformal vector fields on a Riemannian manifold, Balkan J. Geom. Appl. 19, 86-93.
Jost, J., (2002), Riemannian Geometry and Geometric Analysis, Berlin, Germany: Springer-Verlag.
Kashiwada, T., (1968), On conformal Killing tensor, Natur. Sci. Rep. Ochanomizu Univ. 19, 67-74.
Kodaira, K., (1953), On a differential-geometric method in the theory of analytic stacks, Proc. Natl. Acad. Sci. USA 39, 1268-1273.
Lichnerowicz, A., (1958), Geometries des groupes de transformations, Paris, France: Dunod.
Lichnerowicz, A., (1948), Courboure et nombres de Betti dune variete riemannienne compacts, C.R. Acad. Sci. Paris 226, 1678-1680.
Lott, J., (2003), Some geometric properties of the Bakry- Emery- Ricci Tensor, Comment. Math. Helv. 78, 865-883.
Mogi, I., (1950), On harmonic field in Riemannian manifold, Kodai Math. Sem. Rep. 2, 61-66.
Tomonaga, Y., (1950), On Betti numbers of Riemannian spaces, J. Math. Soc. Japan 2, 93-104.
Murat, L., (2009), The Bochner technique and modification of the Ricci Tensor, Ann. Global Anal. Geom. 36, 285-291.
Petersen, P., (1998), Riemannian Geometry, New York, USA: Springer-Verlag.
Wei, G. and Wylie, W., (2009), Comparison geometry for the Bakry-Emery-Ricci tensor, J. Differential Geom. 83, 337-405.
Yano, K., (1952), On harmonic and Killing vector fields, Ann. of Math. 55, 38-45.
Tüm Kaynakçayı Göster
Daha Az Kaynakça Göster
Toplam 15 adet kaynakça vardır.
Ayrıntılar
Birincil Dil
İngilizce
Bölüm
Research Article
Yazarlar
S. Eker
Bu kişi benim
Department of Mathematics, Faculty of Science and Letters, Ağrı ˙Ibrahim Cecen University, 04100, Ağrı, Turkey
Yayımlanma Tarihi
1 Mart 2019
Yayımlandığı Sayı
Yıl 2019
Cilt: 9 Sayı: 1